# Elementary Set Theory, Part I

Publication Year: 1992

Published by: Hong Kong University Press, HKU

#### Cover

#### Title Page, Copyright

#### FOREWORD

The most striking characteristic of modern mathematics is its greater unity and generality. In modern mathematics, the boundaries between different areas have become obscured; very often, what used to be separate and unrelated disciplines are now special cases of a single one; and, amid these far-reaching changes, there have emerged certain basic ...

#### PREFACE

*Elementary Set Theory* is an extension of the lecture notes for the
course 'Fundamental Concepts of Mathematics* given each year to
first-year undergraduate students of mathematics in the University of
Hong Kong since 1959. The purpose of this course, arranged in about
twenty-five lectures, is to provide students of mathematics with the ...

#### CHAPTER 1. STATEMENT CALCULUS

Throughout this chapter, we shall mainly be concerned with statements.
Here we shall briefly describe what we propose to do with them. In the
*statement calculus* (or *propositional calculus*) of this chapter, with the
exception of Sections **K** and **L**, we shall not concern ourselves with the
relation between the subjects and the predicates of the statements. ...

#### CHAPTER 2. SETS

A fundamental concept in mathematics is that of a set. This concept
can be used as a foundation of all known mathematics. In this and the
following chapters, we shall develop some of the basic properties of sets.
In set theory, we shall be dealing with sets of objects. Here we take *objects*
to be simply the individual things of our intuition and our thoughts. ...

#### CHAPTER 3. RELATIONS

We have seen in Section **2 E** that, given any two objects *x* and *y*
there is a set *{x,y}* which has *x* and *y* as its only elements. Moreover,
*{x,y} = {y,x}*; in other words, the order in which the objects *x* and *y*
appear is immaterial to the construction of the set *{x,y}*. For this reason
the set *{x,y}* is called an unordered pair. ...

#### CHAPTER 4. MAPPINGS

Most readers are familiar with the graphical concept of functions.
This involves in general a set *A* of objects called *arguments*, a set *B* of
objects called *values* and an act of associating with each argument in
*A* a unique value in *B*. In elementary calculus, an expression *y = f(x)*
is used to represent an act of associating with each argument *x* (a real ...

E-ISBN-13: 9789882201187

Print-ISBN-13: 9789622090132

Page Count: 80

Publication Year: 1992

OCLC Number: 794700923

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